14th New York Complex Matter Workshop

Saturday December 6, 2014

The 14th New York Complex Matter Workshop will be held December 6, 2014 at Cornell University. The NYCMW will have a slightly different format this year and will include a combination of talks, posters, and "sound bite" research presentations, covering a wide array of problems and research techniques. Our speakers will address a similar topic relating to systems with constraints.

Keynote speaker

Tom Lubensky from the University of Pennsylvania

Additional talks by

Mark Bowick, Syracuse University

Paul McEuen, Cornell University

Chris Santangelo, University of Massachusetts at Amherst (UMASS)

This year will feature a poster session over lunch and prizes for the best "sound-bite" and poster presentations. We are limiting the number of sound bites to 20.

Location

Physical Sciences Building

120 Physical Sciences BuildingCornell University, Ithaca, NY

Parking: There is free parking at the Forest Home GarageGPS: 37 Forest Home Dr, Ithaca (be aware a section of East Ave is closed for construction)Parking Map

Program

Graphene Statistical Mechanics

Mark Bowick, Syracuse University

Abstract: Graphene provides an ideal and unusual system to test the statistical mechanics of thermally fluctuating elastic membranes. The high Young’s modulus of graphene means that thermal fluctuations over even small length scales significantly stiffen the renormalized bending rigidity. I will review fluctuating membranes and emphasize the unique features of graphene. Geometry plays a prominent role here and a full understanding of the geometry-dependent mechanical properties of graphene, including arrays of cuts, may allow the design of a variety of modular elements with desired mechanical properties starting from pure graphene alone.

From Jamming to Topological Surface Phonons

Tom Lubensky, Department of Physics and Astronomy, University of Pennsylvania

Abstract: Frames consisting of nodes connected pairwise by rigid rods or central-force springs, possibly with preferred relative angles controlled by bending forces, are useful models for systems as diverse as architectural structures, crystalline and amorphous solids, sphere packings and granular matter, networks of semi-flexible polymers, and protein structure. The rigidity of these networks depends on the average coordination number z of the nodes: If z is small enough, the frames have internal zero-frequency modes, and they are “floppy”; if z is large enough, they have no internal zero modes and they are rigid. The critical point separating these two regimes occurs at a rigidity threshold, which corresponds closely to what is often referred to as the isostatic point, that for central forces in d-dimensions occurs at coordination number zc = 2d. At and near the rigidity threshold, elastic frames exhibit unique and interesting properties, including extreme sensitivity to boundary conditions, power-law scaling of elastic moduli with (z- zc), and diverging length and time scales.

This talk will explore elastic and mechanical properties and mode structures of model periodic lattices, such as the square and kagome lattices with central-force springs, that are just on verge of mechanical instability. It will discuss the origin and nature of zero modes of these structures under both periodic (PBC) and free boundary conditions (FBC), and it will derive general conditions [1] (a) under which the zero modes under the two boundary conditions are essentially identical and (b) under which phonon modes are gapped with no zero modes in the periodic spectrum but include zero-frequency surface Rayleigh waves in the free spectrum. In the former situation, lattices are generally in a type of critical state that admits states of self-stress in which there can be tension in bars with zero force on any node, and distortions away from that state give rise to surface modes under free boundary conditions whose degree of penetration into the bulk diverges at the critical state. The gapped states have a topological characterization, similar to that of topological insulators, that define the nature of zero-modes at the boundary between systems with different topology.

Graphene kirigami

Paul McEuen, Dept. of Physics and the Kavli Institute at Cornell for Nanoscale Science, Cornell University For centuries, practitioners of the paper arts of origami (“ori”=fold) and kirigami (“kiri”=cut) have created beautiful and complex structures from a simple sheet of paper. Scientists and engineers are beginning to import these ideas and apply them to other materials, and this approach is already proving its extraordinary potential many across disciplines. Here we show that graphene, an atomically thin sheet of carbon atoms, is a perfect starting material for micro- and nanoscale kirigami. We first demonstrate that we can, with the right tools, pick up monolayer graphene and manipulate it like a sheet of paper. This technique allows us to characterize the out-of-plane bending stiffness of graphene for the first time, and we find a bending stiffness thousands of times higher than simple expectations. We show that this surprising result can be explained by the effects of static ripples and/or thermal fluctuations in the membrane. We then apply ideas from kirigami to pattern the graphene into a variety of shapes and explore their properties. These include stretchable electrodes, springs, and robust hinges. This simple but powerful approach promises resilient, customizable, and functional moving parts at the nanoscale.

On form and feel: the mechanics of origami

Chris Santangelo, UMASS AmherstOrigami-inspired materials have emerged as a potentially powerful method to develop mechanical metamaterials, materials that, by virtue of their microstructure, can exhibit effective mechanical properties rare in natural materials. Anecdotally, we know that the mechanical properties of different origami fold patterns can be quite different. I will discuss our recent work on the mechanics of origami, and in particular on a topological classification of fold patterns that captures some generic features of the mechanical response of these structures.